c alculate the rest of the division of 2^n by 3 ; n ∈ N


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Question Number 120469 by mathocean1 last updated on 31/Oct/20

$c a l c u l a t e t h e r e s t o f t h e d i v i s i o n o f$ $2^{n} b y 3; n \in N$
	Answered by mathmax by abdo last updated on 31/Oct/20

	$n = 2 k \Rightarrow 2^{n} = 2^{2 k} = 4^{k} we hsve 4 \approx 1 [3] \Rightarrow 4^{n} \approx 1 [3] \Rightarrow r = 1$ $n = 2 k + 1 \Rightarrow 2^{n} = 2^{2 k + 1} = 2 . 4^{k} we have 4^{k} \approx 1 [3] \Rightarrow 2 . 4^{k} \approx 2 [3] \Rightarrow$ $\Rightarrow r = 2$
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